Theorem nfiota1 5853

Description: Bound-variable hypothesis builder for the iota class. (Contributed by Andrew Salmon, 11-Jul-2011.) (Revised by Mario Carneiro, 15-Oct-2016.)

Assertion

Ref	Expression
nfiota1	|- F/_ x ( iota x ph )

Proof of Theorem nfiota1

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfiota2 5852	. 2 |- ( iota x ph ) = U. { y | A. x ( ph <-> x = y ) }
2		nfaba1 2770	. . 3 |- F/_ x { y | A. x ( ph <-> x = y ) }
3	2	nfuni 4442	. 2 |- F/_ x U. { y | A. x ( ph <-> x = y ) }
4	1, 3	nfcxfr 2762	1 |- F/_ x ( iota x ph )

Syntax hints:   <-> wb 196   A.wal 1481   {cab 2608   F/_wnfc 2751   U.cuni 4436   iotacio 5849

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ral 2917  df-rex 2918  df-sn 4178  df-uni 4437  df-iota 5851

This theorem is referenced by:  iota2df  5875  sniota  5878  opabiota  6261  nfriota1  6618  nfriotad  6619  erovlem  7843  bnj1366  30900  nosupbnd2  31862